RESULTS ON SUBGROUPS OF THE GROUP OF HOMEOMORPHISMS OF THE RATIONAL NUMBERS

Abstract

If G is the group of homeomorphisms of the rationals with usual topology and H ? G is such that |G:H| < 2^x0 then there exists a finite, non-empty subset Y of the rational numbers such that G(Y) ? H ? G^{Y} where G(Y) is the group o all homeomorphisms in G fixing a neighbourhood of Y and G^{Y} is the set-wise stabilizer of Y in G.